rank test; random blocks; hypotheses testing; increasing treatment effect; asymptotic distribution
The testing of the null hypothesis of no treatment effect against the alternative of increasing treatment effect by means of rank statistics is extended from the classical Friedman random blocks model into an unbalanced design allowing treatments not to be applied simultaneously in each random block. The asymptotic normality of the constructed rank test statistic is proved both in the setting not allowing ties and also for models with presence of ties. As a by-product of the proofs a multiple comparisons rule based on rank statistics is obtained for the case when the null hypothesis of no treatment effect is tested against the general alternative of its negation.
 Conover, W. J.: Practical Nonparametric Statistics. Third edition. John Wiley & Sons, Inc., New York 1999.
 Friedman, M.: The use of ranks to avoid the assumption of normality implicit in the analysis of variance
. J. Amer. Statist. Assoc. 32 (1937), 675–701. DOI 10.1080/01621459.1937.10503522
 Hájek, J.: A Course in Noparametric Statistics
. Holden Day, San Francisco 1969. MR 0246467
 Hájek, J., Šidák, Z., Sen, P. K.: Theory of Rank Tests
. Academic Press, New York 1999. MR 1680991
 Lehmann, E. L.: Nonparametrics
. Statistical Methods Based on Ranks. Springer Science and Business Media, New York 2006. MR 2279708
| Zbl 1217.62061